An ice cream truck that plays loud music is circling Bulan's neighborhood. $C(t)$ models the volume of the music (in $\text{dB}$ ) that Bulan hears, $t$ minutes after the truck arrives in her neighborhood. Here, $t$ is entered in radians. $C(t) = -15\cos\left(\dfrac{2\pi}{15}t\right) + 65$ How many minutes after the truck arrives does the volume first reach $75\text{ dB}$ ? Round your final answer to the nearest tenth of a minute.
Explanation: Converting the problem into mathematical terms $C(t) = -15\cos\left({\dfrac{2\pi}{15}}t\right) + 65$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{15}}}=15$ minutes. We want to find the first solution to the equation $C(t)=75$ within the period $0<t<15$. The answer The equation's two solutions within the desired period (rounded to the nearest tenth of a minute) are $5.5$ and $9.5$. Therefore, the volume first reaches $75\text{ dB}$ after $5.5$ minutes.